Tensor network renormalization group study of spin-1 random Heisenberg chains

Abstract

We use a tensor network strong-disorder renormalization group (tSDRG) method to study spin-1 random Heisenberg antiferromagnetic chains. The ground state of the clean spin-1 Heisenberg chain with uniform nearest-neighbor couplings is a gapped phase known as the Haldane phase. Here we consider disordered chains with random couplings, in which the Haldane gap closes in the strong disorder regime. As the randomness strength is increased further and exceeds a certain threshold, the random chain undergoes a phase transition to a critical random-singlet phase. The strong-disorder renormalization group method formulated in terms of a tree tensor network provides an efficient tool for exploring ground-state properties of disordered quantum many-body systems. Using this method we detect the quantum critical point between the gapless Haldane phase and the random-singlet phase via the disorder-averaged string order parameter. We determine the critical exponents related to the average string order parameter, the average end-to-end correlation function and the average bulk spin-spin correlation function, both at the critical point and in the random-singlet phase. Furthermore, we study energy-length scaling properties through the distribution of energy gaps for a finite chain. Our results are in closer agreement with the theoretical predictions than what was found in previous numerical studies. As a benchmark, a comparison between tSDRG results for the average spin correlations of the spin-1/2 random Heisenberg chain with those obtained by using unbiased zero-temperature QMC method is also provided.

10 pages, 12 figures

References in corpus (10)

• The density-matrix renormalization group in the age of matrix product states
• Many body localization and thermalization in quantum statistical mechanics
• A class of quantum many-body states that can be efficiently simulated
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Entanglement renormalization for disordered systems
• Strong disorder renormalization group study of S=1/2 Heisenberg antiferromagnet layers/bilayers with bond randomness, site dilution and dimer dilution
• Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
• The correlation functions of certain random antiferromagnetic spin-1/2 critical chains
• Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain
• Localization of spinons in random Majumdar-Ghosh chains

Cited by in corpus (7)

• Studying dynamics in two-dimensional quantum lattices using tree tensor network states
• Tensor network models of AdS/qCFT
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Tensor-network strong-disorder renormalization groups for random quantum spin systems in two dimensions
• Dynamical properties of the Haldane chain with bond disorder
• Ground state of the S = 1/2 Heisenberg spin chain with random ferro- and antiferromagnetic couplings
• Entanglement-based tensor-network strong-disorder renormalization group